What is the relationship between Maniac and Grayson in Maniac Magee?

As the other educator points out, Maniac and Grayson share a father-son relationship. Grayson is also a mentor and a male role model to Maniac.

When Maniac discovers that Grayson played in the Minor Leagues, he is impressed. The young orphan is even more impressed when he learns that Grayson played as a pitcher. The knowledge that Grayson played in such a pivotal position completely changes Maniac's perspectives about his mentor.

Suddenly, Grayson is no longer just a park maintenance man and someone who lives at the YMCA. Before Grayson knows it, Maniac is begging for stories about his time in the Minors. Grayson begins by telling Maniac how he got his start playing for the Bluefield Bullets in West Virginia.

Maniac is fascinated when he learns that Grayson ended up washing dishes at a restaurant on his first day in Bluefield. Apparently, a gas station attendant played a joke on Grayson. He told Grayson that every rookie got a free meal at the Blue Star restaurant. Upon hearing this, Grayson went over and ordered a sixteen-ounce steak, half a broiled chicken, and two pieces of rhubarb pie. Grayson relates how shocked he was to discover that he'd been played. Accordingly, Grayson eventually spent the day washing dishes to pay for his "free" meal at the Blue Star restaurant.

To hear more about Grayson's early experiences about playing in the Minors, Maniac tags along when the old man goes to work. The young orphan helps Grayson raise a new fence around the children's petting yard. When the park supervisor comes around, Grayson tells him that Maniac is his nephew.

The text tells us that Maniac follows Grayson to work every day after this first collaboration between them. In due time, Maniac can be found working with Grayson at many park tasks. These include mending fences, trimming trees, and patching asphalt. The two also eat all their meals together and spend every day together.

So, the relationship between Maniac and Grayson is one between a mentor and his mentee. Grayson also doubles as a role model and father figure to Maniac. Above all this, Maniac and Grayson are good friends.

A standard way to answer this question is going to say that the relationship between Maniac and Grayson is a father and son type relationship.  Maniac has run away from home, and he is searching for some kind of family.  Grayson, for a short time, fills that role.  He takes Maniac in and acts as a supporting father should.  At times Grayson is a caretaker, and other times Grayson is a friend to Maniac.  Maniac in turn sees Grayson as an authority figure.  Additionally, Maniac sees Grayson as a source of fatherly wisdom about life in general.  

The relationship does change at one point though to become a teacher and student relationship.  That occurs when Maniac decides to teach Grayson how to read.  I believe that Grayson and Maniac are practically made for each other, which is why it is so sad that Grayson dies.  

How does Grayson find Maniac in Maniac Magee?

Maniac looks haggard, dirty, underfed, and just generally pitiable when Grayson finds him.

This happens at the beginning of Chapter 22. Here's how the narrator describes Maniac right as Grayson discovers him:

The kid looked terrible. His clothes were scraps, rags. Wherever his body showed through, it was bony and dirty and scratched.

Maniac has been sleeping in the buffalo pen at the zoo, having run away from Amanda's house after some of her neighbors made it clear that a white kid like him was unwelcome in the East End. When Grayson finds Maniac, the boy has been away from the comforts of the Beale home for quite a while, without meals, without a clean place to rest at night. So it's no wonder that he's ragged and scrawny when the kind old Grayson realizes that there's a kid in the buffalo pen.

Normally a resourceful kid who's great at taking care of himself, Maniac reveals a deeper problem by letting himself become such a mess: he's in despair after being practically run out of the East End neighborhood that he'd loved so much. He's also deeply displeased with himself for allowing Amanda's encyclopedia to be destroyed.